考虑边界效应的非饱和土圆柱孔扩张问题解析

Solution for cylindrical cavity expansion in unsaturated soils considering boundary effect

圆柱孔扩张理论是分析沉桩挤土及旁压试验等岩土工程问题的有效方法,然而已有研究中多假定土体为无限连续介质,当圆柱孔周围存在约束边界时并不适用。采用临界状态模型描述非饱和土的应力-应变关系,在此基础上引入反映土体比体积-吸力关系的液相本构方程,推导了非饱和土中存在固定边界时,圆柱孔扩张问题在不同排水条件下的半解析解。通过计算不同工况,对比分析边界效应、非饱和吸力效应和排水条件对圆柱孔扩张响应的影响。结果表明,受边界效应影响,扩孔压力随着孔径增大而持续增大,这与无边界时扩孔压力趋于某一稳定值的情况有所不同;当圆柱孔扩张相同孔径时,周围固定边界范围越小,所需扩孔压力越大。土体初始吸力越大,扩孔压力也越大,相同应力增量引起的体积压缩量减小,说明土体出现吸力硬化效应。在孔周相同位置处,不排水比排水条件下的土体饱和度高、吸力小,对应的有效应力分量也小;距孔壁越近,该差异越明显。

The cylindrical cavity expansion theory is an effective method to analyze various geotechnical problems,such as pile installations and pressure meter tests.However,most of existing studies which assume that the soil is an infinite medium are not suitable for the case of finite medium.The critical state model is used to describe the stress-strain relationship of unsaturated soils and the constitutive model for water phase which represents the relationship between the specific volume and suction is introduced.With the boundary effects considered,the semi-analytical solutions for cylindrical cavity expansion in unsaturated soil under different drainage conditions are deduced.Intensive parametric studies have been conducted to analyze the effects of boundary,suction and drainage conditions on the results of cavity expansion.The results show that the cavity pressure increases continuously with the increase of cavity radius under the effects of boundary,which is different from the cavity pressure that tends to be a stable value in infinite medium.The greater cavity pressure is required to expand the same cavity radius for a smaller boundary size.In addition,the cavity pressure increases and variation of specific volume caused by the same stress increment decreases with the increase in initial suction,which can be attributed as the suction hardening effect.The saturation of soil at the same position around the cavity is higher,and the suction and effective stress components are lower in the case of undrained condition than drained condition.It is more obvious when the distance from the cavity wall decreases.